Simplify 1/(1+cot(x)^2)

Problem

1/(1+cot2(x))

Solution

1. Identify the Pythagorean identity for the denominator.

2. Apply the identity 1+cot2(x)=csc2(x) to rewrite the expression.

1/(1+cot2(x))=1/csc2(x)

3. Use the reciprocal identity sin(x)=1/csc(x) to simplify the fraction.

1/csc2(x)=sin2(x)

Final Answer

1/(1+cot2(x))=sin2(x)

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